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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_5200.5117', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.30901699437494745, -0.9510565162951535], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-1.0, -1.4081532572346456e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.8090169943749475, -0.5877852522924731], 'algebraic': True, 'analytic_conductor': 24.14869847674626, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '5200.5117', 'coeff_info': ['x^20 - 1', '0.951056516295154 + 0.309016994374947*I', '\\\\zeta_{20}'], 'conductor': 5200, 'conductor_radical': 130, 'conjugate': 'dirichlet_L_5200.1253', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^16', 0, 0, 0, 'a^10', 0, 'a^12', 0, 'a^18', 0, 0, 0, 0, 0, 'a^19', 0, 'a^24', 0, 'a^26', 0, 'a^23', 0, 0, 0, 'a^28', 0, 'a^11', 0, 'a^9', 0, 'a^14', 0, 0, 0, 'a^27', 0, 0, 0, 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'193.9478302330778438991249205208', '194.37448450974761906585714276616', '194.718805721689033969287052587645', '195.55820737148675667977127152880', '196.043641551546629661801021224193', '196.151243035964067929102694229435', '196.95198293147254479066224619991', '197.54641201652918925263035849105', '197.799843918159015865680664443198', '198.11460336895926388907547626261', '199.25046911706550345843928613647', '199.708199533875637341508688119839'], 'prelabel': '1-5200-5200.5117-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.14869847674626, 'root_angle': 0.17570823954725032, 'root_number': '0.450021038443653843220878024168+0.893017953323501458553891183806*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(20)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.922895324370753019942013705438-0.228399338013704435930648813014*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.05484816876', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.59063048601', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.7192336712', 'prec': 40}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 24.14869847674626, 'bad_primes': [2, 5, 13], 'central_character': '5200.5117', 'conductor': 5200, 'conductor_radical': 130, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5200/5117'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-5200-5200.5117-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-5200-5200.5117-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.14869847674626, 'root_angle': 0.17570823954725032, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.05484816876', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_5200.5117', 'Lhash_array': ['dirichlet_L_5200.5117'], 'factors': ['1-5200-5200.5117-r0-0-0'], 'label': '1-5200-5200.5117-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5200/5117'}
Lfunction data - 1-5200-5200.5117-r0-0-0